Universal logic gate utilizing nanotechnology

ABSTRACT

A universal logic gate apparatus is disclosed, which include a plurality of self-assembling chains of nanoparticles having a plurality of resistive connections, wherein the plurality of self-assembling chains of nanoparticles comprise resistive connects utilized to create A plasticity mechanism is also provided, which is based on a plasticity rule for creating stable connections from the plurality of self-assembling chains of nanoparticles for use with the universal, reconfigurable logic gate. The plasticity mechanism can be based, for example, on a 2-dimensional binary input data stream, depending upon design considerations. A circuit is also associated with the plurality of self-assembling chains of nanoparticles, wherein the circuit provides a logic bypass that implements a flip-cycle for second-level logic. Additionally, an extractor logic gate is associated with the plurality of self-assembling chains of nanoparticles, wherein the extractor logic gate provides logic functionalities.

RELATED APPLICATION DATA

This patent application is a divisional of U.S. patent application Ser.No. 11/449,321, entitled “Universal Logic Gate Utilizing Nanotechnology”filed on Jun. 8, 2006 now U.S. Pat. No. 7,420,396, which in turn claimsthe benefit of provisional patent application Ser. No. 60/692,109,entitled “Universal Logic Gate Utilizing Nanotechnology,” which wasfiled on Jun. 17, 2005, the disclosures of which are respectivelyincorporated herein by reference in their entirety.

TECHNICAL FIELD

Embodiments generally relate to the field of nanotechnology, includingnanotechnology-based devices and systems. Embodiments additionallyrelate to logic gate components constructed utilizing nanotechnology.Embodiments additionally relate to self-assembling and repairing methodsand systems.

BACKGROUND

Nanotechnology generally involves technological developments at thenanometer scale (e.g., 0.1-100 nm). The term “nanotechnology” refers tothe manipulation of matter on the scale of the nano-meter (one billionthof a meter). The goal of nanotechnology is to control individual atomsand molecules to create computer chips and other devices that arethousands of times smaller than current technologies permit, or toutilize the molecular properties in more intelligent ways. Beyond beingused in computers and communication devices, nanotechnology could beused to build devices, change the properties of materials and makeadvances in biotechnology.

One example of a nanotechnology-based device/system is the Knowm™network or system, which is described in a U.S. patent and a number ofU.S. patent publications. U.S. Pat. No. 6,889,216, entitled “PhysicalNeural Network Design Incorporating Nanotechnology,” which issued toAlex Nugent on May 3, 2005 generally describes a physical neural networkbased on nanotechnology, including methods thereof. Such a physicalneural network, which can be referred to as a Knowm™ network generallyincludes one or more neuron-like nodes, which are formed from aplurality of interconnected nanoconnections formed from nanoconductors.Such connections constitute Knowm™ connections. Each neuron-like nodesums one or more input signals and generates one or more output signalsbased on a threshold associated with the input signal.

The Knowm™ device physical neural network also includes a connectionnetwork formed from the interconnected nanoconnections, such that theinterconnected nanoconnections used thereof by one or more of theneuron-like nodes are strengthened or weakened according to anapplication of an electric field, variations in frequency, and so forth.U.S. Pat. No. 6,889,216 is incorporated herein by reference.

Another example of a Knowm™ network or system is described in U.S.Patent Publication No. 20030236760, entitled “Multi-layer Training in aPhysical Neural Network Formed Utilizing Nanotechnology,” by inventorAlex Nugent, which was published on Dec. 25, 2003. U.S. PatentPublication No. 20030236760 generally describes methods and systems fortraining at least one connection network located between neuron layerswithin a multi-layer physical neural network (e.g., a Knowm™ network ordevice). The multi-layer physical neural network described in U.S.Patent Publication No. 20030236760 can be formed with a plurality ofinputs and a plurality outputs thereof, wherein the multi-layer physicalneural network comprises a plurality of layers therein, such that eachlayer thereof comprises at least one connection network and at least oneassociated neuron.

Thereafter, a training wave, as further described in U.S. PatentPublication No. 20030236760, can be initiated across one or moreconnection networks associated with an initial layer of the multi-layerphysical neural network which propagates thereafter through succeedingconnection networks of succeeding layers of the multi-layer physicalneural network by successively closing and opening at least one switchassociated with each layer of the multi-layer physical neural network.At least one feedback signal thereof can be automatically provided toeach preceding connection network associated with each preceding layerthereof to strengthen or weaken nanoconnections associated with eachconnection network of the multi-layer physical neural network. U.S.Patent Publication No. 20030236760 is incorporated herein by reference.

A further example of a Knowm™ network or system is described in U.S.Patent Publication No. 20040039717, entitled High-density synapse chipusing nanoparticles” by inventor Alex Nugent. U.S. Patent PublicationNo. 20040039717 published on Feb. 26, 2004 and generally describes aphysical neural network synapse chip (i.e., a Knowm™ chip) and a methodfor forming such a synapse chip. The synapse or Knowm™ chip can beconfigured to include an input layer comprising a plurality of inputelectrodes and an output layer comprising a plurality of outputelectrodes, such that the output electrodes are located perpendicular tothe input electrodes. A gap is generally formed between the input layerand the output layer.

A solution can then be provided which is prepared from a plurality ofnanoconductors and a dielectric solvent. The solution is located withinthe gap, such that an electric field is applied across the gap from theinput layer to the output layer to form nanoconnections of a physicalneural network implemented by the synapse chip. Such a gap can thus beconfigured as an electrode gap. The input electrodes can be configuredas an array of input electrodes, while the output electrodes can beconfigured as an array of output electrodes. U.S. Patent Publication No.20040039717 is also incorporated herein by reference.

A further example of a Knowm™ network or system is disclosed in U.S.Patent Publication No. 20040153426, entitled “Physical Neural NetworkLiquid State Machine Utilizing Nanotechnology,” by inventor Alex Nugent,which was published on Aug. 5, 2004. U.S. Patent Publication No.20040153426 generally discloses a physical neural network (i.e., aKnowm™ network), which functions as a liquid state machine.

The physical neural network described in U.S. Patent Publication No.20040153426 can be configured from molecular connections located withina dielectric solvent between pre-synaptic and post-synaptic electrodesthereof, such that the molecular connections are strengthened orweakened according to an application of an electric field or a frequencythereof to provide physical neural network connections thereof. Asupervised learning mechanism is associated with the liquid statemachine, whereby connections strengths of the molecular connections aredetermined by pre-synaptic and post-synaptic activity respectivelyassociated with the pre-synaptic and post-synaptic electrodes, whereinthe liquid state machine comprises a dynamic fading memory mechanism.U.S. Patent Publication No. 20040153426 is also incorporated herein byreference.

A further example of a Knowm™ network or system is disclosed in U.S.Patent Publication No. 20040162796, entitled “Application of Hebbian andanti-Hebbian Learning to Nanotechnology-based Physical Neural Networks”by inventor Alex Nugent, which published on Aug. 19, 2004. U.S. PatentPublication No. 20040162796 generally discloses a physical neuralnetwork (i.e., Knowm™ network) configured utilizing nanotechnology. TheKnowm™ network disclosed in U.S. Patent Publication No. 20040162796includes a plurality of molecular conductors (e.g., nanoconductors)which form neural connections between pre-synaptic and post-synapticcomponents of the physical neural network.

Additionally, a learning mechanism can be applied, which implementsHebbian and anti-hebbian learning via the physical neural network. Sucha learning mechanism can utilize a voltage gradient or voltage gradientdependencies to implement Hebbian and/or anti-Hebbian (AHAH) plasticitywithin the physical neural network. The learning mechanism can alsoutilize pre-synaptic and post-synaptic frequencies to provide Hebbianand/or anti-Hebbian learning within the physical neural network. U.S.Patent Publication No. 20040162796 is incorporated herein by reference.

An additional example of a Knowm™ network or device is disclosed in U.S.Patent Publication No. 20040193558, entitled “Adaptive Neural NetworkUtilizing Nanotechnology-based Components” by Alex Nugent, whichpublished on Sep. 30, 2004. U.S. Patent Publication No. 20040193558generally describes methods and systems for modifying at least onesynapse of a physical neural network (i.e., a Knowm™ network). Thephysical neural or Knowm™ network described in U.S. Patent PublicationNo. 20040193558 can be implemented as an adaptive neural network, whichincludes one or more neurons and one or more synapses thereof.

The neurons and synapses are formed from a plurality of nanoparticlesdisposed within a dielectric solution in association with one or morepre-synaptic electrodes and one or more post-synaptic electrodes and anapplied electric field. At least one pulse can be generated from one ormore of the neurons to one or more of the pre-synaptic electrodes of asucceeding neuron and one or more post-synaptic electrodes of one ormore of the neurons of the physical neural network, therebystrengthening at least one nanoparticle of a plurality of nanoparticlesdisposed within the dielectric solution and at least one synapsethereof. U.S. Patent Publication No. 20040193558 is incorporated hereinby reference.

Another example of a Knowm™ network or device is disclosed U.S. PatentPublication No. 20050015351, entitled “Nanotechnology Neural NetworkMethods and Systems” by inventor Alex Nugent, which published on Jan.20, 2005. U.S. Patent Publication No. 20050015351 generally discloses aphysical neural network (i.e., a Knowm™ network), which constitutes aconnection network comprising a plurality of molecular conductingconnections suspended within a connection gap formed between one or moreinput electrodes and one or more output electrodes. One or moremolecular connections of the molecular conducting connections can bestrengthened or weakened according to an application of an electricfield, frequency, and the like across the connection gap.

Thus, a plurality of physical neurons can be formed from the molecularconducting connections of the connection network. Additionally, a gatecan be located adjacent the connection gap and which comes into contactwith the connection network. The gate can be connected to logiccircuitry which can activate or deactivate individual physical neuronsamong the plurality of physical neurons. U.S. Patent Publication No.20050015351 is incorporated herein by reference. Based on the foregoingit can be appreciated that a Knowm™ connection(s), which forms the heartof a Knowm™ network can be thought of as constituting an electro-kineticinduced particle chain.

As transistor densities on modern integrated electronic chips increase,there is a growing trend toward reconfigurable architectures. Ratherthan implementing application specific integrated circuits (ASIC), it ispreferred that a design be deployed on programmable logic devices. Themove in such a direction is creating a growing trend toward an IP-baseddevelopment process, where circuits are defined by their programmingroutine rather than the actual physical layout. Rather than implementinga program to run on a processor, for example, a chip may process aprogram to build the processor.

In view of the foregoing developments in nanotechnology and the need forreconfigurable architectures it is believed that one solution towardcreating such technology involves the implementation of genericself-assembling nanotechnology logic gate components and systems, ofwhich none are known to have been successfully implemented in commercialelectronics. A universal logic gate is therefore disclosed herein, whichsolves this increasing need and can be fabricated with modernfabrication processes.

BRIEF SUMMARY

The following summary is provided to facilitate an understanding of someof the innovative features unique to the embodiments, and is notintended to be a full description. A full appreciation of the variousaspects of the embodiments can be gained by taking the entirespecification, claims, drawings, and abstract as a whole.

It is, therefore, one aspect of the present invention to provide for adevice for an improved nanotechnology-based electronic and computingcomponent.

It is another aspect of the present invention to provide for a universallogic gate, which can be formed utilizing self-assemblingnanotechnology.

It is yet another aspect of the present invention to provide a mechanismfor the reconfiguration of the universal logic gate.

It is yet another aspect of the present invention to provide acircuit-level implementation of a universal logic gate.

The above and other aspects can be achieved as is now described. Auniversal logic gate apparatus is disclosed, which include a pluralityof self-assembling chains of nanoparticles having a plurality ofresistive connections, wherein the plurality of self-assembling chainsof nanoparticles comprise resistive connects utilized to create Aplasticity mechanism is also provided, which is based on a plasticityrule for creating stable connections from the plurality ofself-assembling chains of nanoparticles for use with the universal,reconfigurable logic gate. The plasticity mechanism can be based, forexample, on a 2-dimensional binary input data stream, depending upondesign considerations. A circuit is also associated with the pluralityof self-assembling chains of nanoparticles, wherein the circuit providesa logic bypass that implements a flip-cycle for second-level logic.Additionally, an extractor logic gate is associated with the pluralityof self-assembling chains of nanoparticles, wherein the extractor logicgate provides logic functionalities.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates a graphical representation of a plasticity rule,which can be implemented in accordance with an embodiment;

FIG. 2 illustrates a Knowm-Capacitor circuit, which can be implementedin accordance with one embodiment;

FIGS. 3( a)-3(d) illustrate circuit layout configurations, which can beimplemented in accordance with one or more embodiments;

FIG. 4 illustrates evaluate and feedback phase frames, which may begenerated in accordance with one or more embodiments;

FIG. 5 illustrates output/evaluate and flip/lock phase representations,which can be implemented in accordance with a first circuit layoutconfiguration;

FIG. 6 illustrates output/evaluate and flip/lock phase representations,which can be implemented in accordance with a second circuit layoutconfiguration;

FIG. 7 illustrates output/evaluate and flip/lock phase representations,which can be implemented in accordance with a third circuit layoutconfiguration;

FIG. 8 illustrates a schematic diagram of a circuit, which can beimplemented in accordance with one embodiment;

FIG. 9 illustrates a schematic diagram of a circuit, which can beimplemented in accordance with another embodiment;

FIG. 10 illustrates a schematic diagram of a circuit, which can beimplemented in accordance with an alternative embodiment;

FIG. 11 illustrates a schematic diagram of a circuit, which can beimplemented in accordance with an embodiment;

FIG. 12 illustrates a schematic diagram of a circuit, which can beimplemented in accordance with an alternative embodiment;

FIG. 13 illustrates a block-level circuit diagram, which can beimplemented in accordance with an embodiment;

FIGS. 14 and 15 illustrate a high-level block diagram of a system forindependent component analysis, which can be implemented in accordancewith a preferred embodiment;

FIG. 16 illustrates a configuration that includes a neuron with synapseinputs, in accordance with one embodiment;

FIG. 17 illustrates a system of neurons and a logic gate, in accordancewith another embodiment;

FIG. 18 illustrates a system of neurons and logic gates, in accordancewith a further embodiment;

FIG. 19 illustrates a system of neurons and logic gates in accordancewith another embodiment; and

FIG. 20 illustrates a universal logic gate system that can beimplemented in accordance with a preferred embodiment.

DETAILED DESCRIPTION

The particular values and configurations discussed in these non-limitingexamples can be varied and are cited merely to illustrate one or moreembodiments.

Dielectrophoresis (DEP)

When a particle is suspended in a solution and subjected to an electricfield, the electric field induces a polarization in the particle. If thefield is homogeneous, the induced dipole aligns in the direction of thefield. If the field is inhomogeneous, the particle will experience aforce. The direction of the force is determined by the dielectricproperties of the particle and suspension. If the particle is morepolarizable than the surrounding medium, the particle will feel a forcein the direction of increasing field gradient, which is termed PositiveDEP. On the other hand, negative DEP results when the medium is morepolarizable than the particle.

At low frequencies, charge accumulation at the particle/medium boundarycontributes to the induced dipole, which is referred to as theMaxwell-Wagner interfacial polarization and is a function of theparticle and medium conductivity. As the frequency is increased, thisterm of the polarization has increasingly less of an effect, as themobile charges do not have time to move an appreciable distance. For thecase of a spherical particle, the time-averaged DEP force can beprovided by equation (1) as indicated below:

$\begin{matrix}{{\overset{\rightarrow}{F}}_{dep} = {2\pi\; r^{3}ɛ_{0}ɛ_{m}{{Re}\left\lbrack \frac{ɛ_{p}^{*} - ɛ_{m}^{*}}{ɛ_{p}^{*} - {2ɛ_{m}^{*}}} \right\rbrack}{\nabla\; E^{2}}}} & (1)\end{matrix}$

For any geometry other than a sphere or ellipsoid, calculating the DEPforce is not trivial, and the applicability of equation 1 requires theparticle radius to be small compared to the changes in the gradient ofthe energy density (∇E²).

A conducting particle in a non-conducting liquid or gel will generallyfeel an attractive force toward the direction of increasing electricfield gradient. As the frequency of the applied electric field isincreased, the force transitions from an attractive to a repulsiveforce. Although it is possible to use lower frequencies to attract aparticle and higher frequencies to repel in such a way as to build andbreak nanoconnections, in the present disclosure we utilize a lowerfrequency, attractive force, to build connections and increasing entropyto break connections.

Our basic requirement, which is detailed in this disclosure, is simplythat an attractive force be applied to the particle, bringing it incontact with electrodes and bridging an electrode gap. As long as theapplication of the field gradient results in an increased probability ofconnection formation, our requirements are met. Indeed, this is the caseand has been demonstrated experimentally by a number of independentorganizations.

The Plasticity Rule

Referring now to FIG. 1, illustrated a graph 100, which demonstrates aplasticity rule, which upon one or more embodiments can be based. Graph100 generally depicts a curve 103 plotted with respect to an axis 101and an axis 102. Axis 101 generally represents f(y) while axis 102represents the variable “y” (i.e., y-data). Thus, graph 100 illustratesa plot of y data versus f(y). Two different states 105 and 104 are alsoindicated in graph 100, where state 105 is a “negative” state orcondition and state 104 is a “positive” state or condition. Thus, aportion 109 of curve 103 is associated with state 105, while a portion111 of curve 103 is associated with state 104. Curve 103 can begenerated based on a plasticity rule. The following plasticity rule asindicated by equation (2) below, when applied to the weights of a neuronunder the influence of a data stream, has been shown to extract theindependent components of the data stream:w _(t+1) =w _(t) +lxf(y)  (2)

In equation (2) above, the variable l represents a small positiveconstant (learning rate), while f(y) represents a non-linear function ofthe total activation of the neuron, y={right arrow over (W)}{right arrowover (x)}, where {right arrow over (W)} is a weight vector and {rightarrow over (x)} an input vector. In the implementation of this rule in aphysical neural network, {right arrow over (W)} represents a matrix ofKnowm™ synapses, {right arrow over (x)} is applied via voltage pulses,and y is the total activation from the synapses. The variable l, thelearning rate, is controlled by a combination of solution viscosity,temperature and operating voltage, and possibly other factors effectingthe physical movement of nanoparticles in a liquid or gel solution.

There are many mathematical rules that have been found to extractindependent components. For a physical embodiment, it is necessary tofind a rule that can be emulated through device physics and particleinteractions. Equation (2) satisfies such criteria. The embodimentsdisclosed herein generally discuss how such a rule can be mapped to aphysical process and controlled electronically. To understand thismapping, it is necessary to discuss a theory used to describe a Knowm™Connection, which can be termed Plastic Probability Theory (PPT). PPT isa way of describing the evolution of a discrete-state synapse viaapplied plasticity rules.

Discrete-State Synapses

Consider a synapse composed of a discrete number of conducting channels,where each channel can be in an “on” or an “off” state. Further considera plasticity rule capable of modification to the number of conductingchannels. We will refer to a conducting channel as open and anon-conducting channel as closed.

The probability at any given time increment that a channel will go fromclosed to open is considered negligible outside the influence ofplasticity. In other words, the only way a channel will ever go fromclosed to open is by the influence of plasticity. The probability that achannel will go from open to closed at any given time increment is givenby a function, E(T), which can be attributed to random thermal motionand is a function of temperature.

Given a total of No open channels, out of N total channels, the updateto the connection can be given as the difference between the plasticupdate, P, and the thermal breakdown, B. The plastic update and thethermal breakdown are dependant on the number of open channels. However,the plastic update can only act on closed channels. In other words, achannel, once opened, can only be closed. If it is open, the probabilityof closing is given by E(T) as indicated in equations (3) below:B=NoE(T)P=(N−No)·H(No)ΔNo=P−B=(N−No)·H(No)−NoE(T)  (3)

In equations (3) indicated above, H(No) represents a PlasticityProbability Field (PPF), which will be discussed shortly. The stablepoints of equations (3) occur when the plastic update equals the thermalbreakdown. Solving for the PPF we have:

$\begin{matrix}{{H({No})} = \frac{{NoE}(T)}{N - {No}}} & (4)\end{matrix}$

For a given thermal breakdown probability, E(T), equation (4) providesthe minimum Instantaneous Probability (IP) necessary to oppose thethermal breakdown. An IP less than that given by equation (4) can resultin the loss of open channels. An IP greater than equation (4) can resultin a gain of open channels. To find the stable points a specific PPFshould be selected. Consider the following PPF provided by equation (5):

$\begin{matrix}{{H({No})} = {\alpha\;{No}\;{\mathbb{e}}^{- \frac{{No}^{2}}{2\sigma^{2}}}}} & (5)\end{matrix}$

For a given No, equation (5) provides the IP that a closed channel willopen. If equations (4) and (5) are graphed, their intersectionrepresents the equilibrium number of open channels, No.

In a Knowm™ connection, a closed channel can be seen as the absence of anano-connection or particle bridge. An open channel is a particle, orchain of particles, providing one conducting path between pre- andpost-synaptic electrodes. The force felt by a particle in a liquidsuspension is a combination of many forces. In many circumstances we mayneglect all but two, which we will utilize to both weaken and strengthenKnowm™ connections. First, we have random thermal motion, which acts toincrease the entropy of particles, spreading them out, and in theprocess breaking any Knowm™ connections formed. Second, we have anelectro-kinetic force, which attracts the particles to the electrode gapvia dipole-induced electrostatic forces.

Plastic Probability Fields

Consider a Knowm™ synapse. The dielectrophoretic force causes theaggregation of nanoparticles to areas of high field gradient. This leadsto nanowires bridging the electrode gap formed from pre- andpost-synaptic electrodes. If the particles are conducting, the localelectric field breaks down, which inhibits the growth of neighboringwires. This results in a set number of possible connections. Withoutthermal breakdown, i.e. the force of random thermal collisions, thewires would remain indefinitely and eventually reach the maximumpossible, N. Under the influence of thermal breakdown, however, theconnection will not reach the maximum number of channels, but insteadachieves a balance between thermal degradation and plastic updates.

A Plastic Probability Field (PPF) is a function that gives theprobability that a channel will go from closed to open over a particularincrement of time. The reason the PPF function is a field instead ofjust a single value is that this probability can (and should) change asa function of the post-synaptic activation. In addition, a PPF does notobey most of the usual notions of probability functions, likenormalization and a continuous derivative. The only functionalrequirement is that the PPF never attain a value greater than 1 or lessthan zero.

As an example, suppose a connection is composed of N=10 channels. Attime step t, 5 of the channels are open (No=5). If the PPF is given as

${H({No})} = {\frac{1}{10}{No}}$then there will be a 50% probability that each of the closed channelswill open. In the absence of thermal break down, we would thereforeexpect about 7 or 8 channels to be open at time step 6. If theprobability of breakdown was P_(f)=0.5, then on average no new channelswould form and the connection will have reached a stable state.

Implementation of Equation (2) as a Plastic Probability Field

Equation (1) includes two basic features that should be taken intoaccount in the physical implementation. First, as the magnitude of theactivation becomes large, the update to the connection becomesnegligible. Second, it is required that the update rule be capable ofre-enforcing two separate states, which can be referred to as the (+)state and (−) state, or State 1 and State 2, respectively. Examples ofsuch variations in state are illustrated in FIG. 1, with respect tostates 104 and 105. In FIG. 1, each state 104 and 105 represents oneside of zero. To aid in understanding of the embodiments disclosedherein, however, it may help to realize that positive and negative aresimply two distinct states, such as A and B or “On” and “Off”. In otherwords a connection can be treated as possessing at least two aspects: amagnitude and a state.

The form of the plasticity rule implemented herein requires amultiplication of the form: {right arrow over (W)}{right arrow over (x)}and x·f(y). The input, x, can be implemented in the form of binaryvoltages, on and off or 1 and 0. In general, On can represent anelectrode that has been raised to the supply voltage. Off can representan electrode that has been grounded. Alternately, and perhaps moreclearly these states can be referred to as (+) and (−), or, for example,simply State 1 and State 2. Likewise, y is also the result of a seriesof explicit multiplications as indicated by equation (6) below:y=w ₁ x ₁ +w ₂ x ₂ +w ₃ x ₃ + . . . +w _(n) x _(n) ={right arrow over(W)}{right arrow over (x)}  (6)

The rules of multiplication, when dealing with numbers of complimentarystates can be represented by the following group of equations (7):A(−B)=(−A)B=−ABAB=BA(−A)(−B)=AB  (7)

For a Knowm™ implementation of equation (2), each Knowm synapsepreferably possesses a distinct state, and for that state to effectivelymultiply itself with the input state. In addition, the update to theneuron should follow the rules of multiplication as well: If the outputof the neuron falls in the (+) state, for example, then the connectionneeds to be modified in such a way to enforce the connections ability totransform the current input state to the current output state. This canonly be done by multiplication with the input and must be provided inthe form of a feedback mechanism that applies an electro-kinetic forceto attract the particles to the electrode gap, or the absence of anelectro-kinetic force so increasing entropy may weaken the connection.

If, under the frequency spectrum of the applied electric fields, theparticle feels a positive DEP force, then this force is proportional tothe square of the energy density, as provided by equation (1). This canalternately be represented by a pre- and post-synaptic voltage, asindicated by equation (8) below:∇|E| ² =∇|V _(pre) −V _(post)|²  (8)

The exact positions of every particle, as well as all of the forcesapplied to it, are not known. A computationally tractable model mustconsider time-averaged approximations. Random thermal motion seeks todisperse the particles through the solution. The application of avoltage difference will increase the probability that a particle willbridge the gap between pre- and post-synaptic electrodes. As a firstapproximation, we may treat the instantaneous probability that aconnection will form, or a conduction channel will open, as proportionalto the square of the voltage difference between pre- and post-synapticelectrodes. The accumulation of probability is proportional to theintegral of pre- and post-synaptic voltages over one evaluate/feedbackcycle, a cycle that will now be discussed.

Evaluate-Feedback Cycle

Consider one Knowm™ Connection, formed between pre-synaptic electrode“A” and post-synaptic electrode “B”. Given the inherently unstablenature of the connection in a liquid, we must provide a mechanism tostabilize the connection at a particular value while simultaneouslymonitoring the connection strength. Once the connection is at thedesired strength, we must either continually provide the feedbackmechanism to keep the connection stable, or else freeze the solution soas to prevent thermal breakdown. As previously discussed, theapplication of an activity-dependant plasticity rule can be utilized asa mechanism for setting or designating connection strengths. Such aplasticity rule, as applied to a Knowm™ connection, preferably operateson pre- and post-synaptic voltages.

To compute a post-synaptic activation, one must “evaluate” theconnections. That is, a particular input vector must be applied topre-synaptic electrodes and the post-synaptic electrode must integratethe individual contribution to form the post-synaptic activation. Thisactivation should produce a post-synaptic voltage. The post-synapticvoltage can then be utilized to apply the desired plasticity rule. Toaccomplish this, the evaluate phase can be separated from the feedbackphase. The evaluate and feedback phases may further be divided, so as toprovide for correct initial conditions.

For the moment, we will assume initial conditions are correctly set. Theaccumulated probability over both the evaluate and feedback phase isgenerally responsible for the connection update. By separating theprocess into two phases, we acquire the two behaviors necessary for asuccessful integration of equation (2). The decreasing update as afunction of activity is provided through the “evaluate” phase while thecorrect update sign is accomplished with the feedback phase. Todemonstrate such a functionality, consider a simple Knowm-Capacitorcircuit 200, as illustrated by FIG. 2.

In general, the Knowm-Capacitor circuit 200 depicted in FIG. 2 includesa Knowm™ connection 202 disposed between a pre-synaptic input 209 andpost-synaptic output 202 thereof. Note that the Knowm-Capacitor circuit200 is connected to a capacitor 204 at the post-synaptic output 202.Capacitor 204 is in turn connected to a ground 208. The Knowm™connection 202 can be thought of as constituting an electro-kineticinduced particle chain. The configuration of circuit 200 is presentedherein for illustrative and exemplary purposes only. It can beappreciated that variations to circuit 200 can be implemented, whilestill maintaining the spirit and scope of the embodiments disclosedherein.

At a time t=0, both pre- and post-synaptic voltages are set to zero. Ifthe pre-synaptic input 209 is raised to a positive value, then thepost-synaptic voltage at the post-synaptic output 211 will begin to riseat a rate determined by the strength of the Knowm™ connection 202. Thestronger the connection(s) thereof, the faster the post-synaptic voltageat the post-synaptic output 211 will equilibrate with the pre-synapticvoltage. Recall that the update to the Knowm™ connection 202, as givenby a probability that a conducting channel will open, is given by thesquare of the difference between the pre- and post-synaptic voltage,integrated over the time period of interest. If we only consider theevaluate phase, then it is apparent that as the Knowm™ connection 202grows stronger, and the activity increases, the accumulated probabilitybecomes smaller and approaches zero.

If, for instance, a series of input voltage pulses is applied at thepre-synaptic input 209, then the Knowm™ connection 202 would equilibrateto a value proportional to total pre-synaptic activation. This couldprove a valuable electronic filter. As it stands, the feedback mechanismwould not mirror the desired plasticity rule. To understand this,consider that a connection formed from the dielectrophoretic assembly ofparticles in a suspension does not inherently possess two states. Theconnection possesses a resistance somewhere between a minimum intrinsicresistance (maximum particles bridging gap) and a maximum intrinsicresistance (no particles bridging gap). To build a system capable of4-quadrant synaptic multiplication, there are 3 basic electrodearrangements. In each arrangement, there also exists more than onefeedback mechanism capable of emulating the plasticity rule. We willdiscuss these three electrode arrangements, as well as the variousfeedback circuitry necessary to provide the required feedback. In allcases, a feedback phase is required, in addition to the evaluate phase,to insure proper connection modification. However, to understand thefeedback stage, it is necessary to discuss a two-state Knowm™connection.

Because a Knowm™ connection does not inherently posses two states, it isnecessary to build the two states into the circuitry. We can create aKnowm™ synapse by combining two or more Knowm™ connections. Take forinstance the case of one pre-synaptic electrode and two post-synapticelectrodes, an arrangement that can be referred to as configuration 1,which is depicted in FIG. 3( a), for example, as circuit layout 302.

FIGS. 3( a)-3(d) illustrate circuit layout configurations 302, 301, and303, which can be implemented in accordance with one or moreembodiments. Layout 302 of configuration 1 depicted in FIG. 3( a), forexample, generally includes an A circuit 325 and a B circuit 324. Anelectrode 321 is connected to B circuit 324, while electrodes 322 and323 are connected to A circuit 325. Electrode 322 can constitute apost-synaptic electrode 1 (PSE1), while electrode 323 can constitute apost-synaptic electrode 2 (PSE2).

The PSE1 322 can be arbitrarily assigned to State 1, while PSE2 323 isarbitrarily assigned to State 2. During the evaluate phase, thepost-Synaptic electrode with the higher voltage is considered the“winner” and feedback circuitry (i.e., to be discussed herein) saturatesthe voltages. We may view the Knowm™ connection connecting the input tothe PSE 1 322 as C11 and the connection between the input and PSE 2 323as C12.

The pre-synaptic voltage may be used to encode the state of the input. Apositive voltage may arbitrarily be assigned to state 1 and a zerovoltage to state 2. If, during the evaluate phase, the pre-synapticinput is positive, then the synapse connecting the input to PSE1 andPSE2 (remember that each synapse is now represented by two Knowm™connections) is considered to be positive if the connection facilitatesthe transfer of an input in state 1 to a post-synaptic output in state1. Likewise, if the input is in state 2, then the connection isconsidered positive if the connection facilitates the transfer of thepost-synaptic output to state 2. This is simply a restatement of therules of multiplication, as outlined in equation 6. The following Table1 illustrates these features:

TABLE 1 Pre-Synaptic Post-Synaptic State State Connection state 1 1 1 12 2 2 2 1 2 1 2

A synapse may not necessarily facilitate the transfer of thepre-synaptic state to the post-synaptic state. In this case, thepost-synaptic state was determined by the summation of individualactivations from all other synapses. If a synapse state is in conflictwith the transfer of the pre-synaptic state to the post-synaptic state,then according to the above mentioned plasticity rule, the connectionshould be modified in a direction opposite its current state.

For electrode configuration 1 of circuit layout 302, if C12 was a strongconnection (i.e., one with many conducting channels) and C11 was weak,then the connection could be considered to be in State 2. This isbecause an input in state 1 (i.e., a positive input voltage) wouldmaximally affect PSE2, raising its voltage at a larger rate than C11could raise PSE1. Correspondingly, an input in state 2 (zero inputvoltage) would maximally affect PSE1 because PSE2 would receive astronger pull to ground. The PSE1 voltage would consequently be higher,forcing the neuron into state 1. Thus we have the case that a connectionwith C12>C11 facilitates the state transfers: 1→2 and 2→1. This isconsistence with a connection in state 2. One can demonstrate with thesame arguments that a synapse with C11>C12 is consistent with aconnection in state 1.

We may now consider the overall synaptic update as a function ofpost-synaptic activation on PSE1 and PSE2, and show that the functionalform matches that required by the above mentioned plasticity rule. Forillustrative purposes, consider the case of a synapse in state 1 underinputs from both state 1 and state 2. Note that we must consider theupdates to both C11 and C12, as it is only their relative strengths thatdetermine the sign of the connection. The update to the synapse can begiven as indicated by equation (9) below:ΔW=N _(C)((A _(C11) −A _(E))−(A _(Cl2) −A _(E)))  (9)

As indicated by equation (9), the variable A_(C11) represents theaccumulation of connection formation probability on C11 and A_(E) is the(negative) accumulation due to random thermal motion. Note that becausea differential pair represents the connection, the negative accumulationdue to random thermal motion cancels out. Also note that when C11 equalsC12 (if we consider a neuron with only one input, otherwise theactivation is a function of all synapses), the accumulation on C11cancels the accumulation on C12 and the update is zero. Likewise, ifC11>>C12 or C12>>C11, the accumulation for C11 equals the accumulationfor C12 and again the accumulation cancels out, resulting in zerooverall update. This last statement can only be understood if oneconsiders an entire evaluate/feedback cycle. The specificcharacteristics of the feedback cycle will be discussed shortly.

One important detail should be mentioned. Although the negativeaccumulation due to random thermal motion cancels out in equation (9),this does not mean that the individual connection has not received thenegative accumulation. The accumulation from plastic updates cancels theaccumulation from random thermal motion. Even without an explicitplastic update, a residual force is needed to keep the particles in thevicinity of the electrode gap. Otherwise a connection would have verylittle chance of forming. We provide this residual force, and controlit, by setting the periods of the evaluate and feedback phase. Forexample, by doubling the period of the evaluate and feedback phase, wedouble the probability that the particle will bridge the electrode gap.

A similar result can also be achieved by increasing the supply voltage,and thereby increasing the force on the particle while maintaining thesame evaluate and feedback periods. This could be advantageous becauseincreasing the period will increase the time of computation. Moreaspects of the rule may be controlled electronically by varying theratio of evaluate and feedback periods. For example, by increasing thefeedback phase while maintaining the evaluate phase, the effective“width” of the rule can be narrowed. Such an operation in turn allowsthe rule to better separate closely adjacent features in the input dataspace.

It can be appreciated that such electronic control over the plasticityrule is extremely beneficial. The control will allow the same chip toprocess many different types of data sets, and for the feedback dynamicsto be modified on-the-fly to account for variations in parameters suchas temperature, processing speed, and input data statistics.

The feedback phase can now be discussed in greater detail. Considerthree consecutive inputs, each in State 1, applied to a connection instate 1. Also consider an arbitrary initial synapse value such asC11=100 gΩ and C12=101 gΩ. During the application of the first inputduring the evaluation phase, PSE1 would receive a slightly highercurrent flux. This difference will be amplified over the course of theevaluate phase until the post-synaptic output is saturated in state 1,or PSE1=1 and PSE2=0. The relative difference between the current fluxon PSE1 and PSE2 determine the time required for the feedback circuitryto saturate the voltages in complimentary states. If the difference isinitially minute, it could take the entire evaluate phase. If theinitial difference is large, the voltages will saturate very quickly,with plenty of time left in the evaluate phase.

Note that in FIGS. 3( b) and 3(c), circuit layouts 301 and 303 are alsoillustrated, which represents variations to the circuit layout 302 orconfiguration 1. Circuit layout 301 thus represents a configuration 2,which is discussed in greater detail herein, while circuit layout 303represents a configuration 3. Circuit layout 301 or configuration 2generally includes a B circuit 314 and an A circuit 315. Electrodes 311and 312 are connected to B circuit 314, while an electrode 313 isconnected to A circuit 315. A Knowm™ connection 380 can be formedbetween electrode 311 and 313. Similarly, a Knowm™ connection can beformed between electrode 313 and electrode 312. In circuit layout 303 ofconfiguration 3, a B circuit 335 is provided along with an A circuit336.

Electrodes 331 and 332 are connected to the B circuit 335, whileelectrodes 333 and 334 are connected to A circuit 136. A Knowm™connection 390 is generally formed between electrode 331 and electrode334. Similarly, a Knowm™ connection 392 can be formed between electrode334 and 332. Similar Knowm™ connections although not depicted in FIG. 3(c) are generally formed between electrode 331 and electrode 333 andbetween electrode 332 and electrode 333. A detailed side view 397 ofKnowm™ connection 390 is indicated by FIG. 3( d). Note that in FIGS. 3(c) and 3(d), identical or similar parts or elements are generallyindicated by identical reference numerals.

FIG. 4 illustrates evaluate and feedback phase frames 400, 402 and 404which may be generated in accordance with one or more embodiments.Frames 400, 402, 404 can also be designated as respective frames A, B,C. Returning to the foregoing example, during the evaluate phase, C12can receive a larger accumulated probability of connection formation, asdepicted by the shaded region in frame A of FIG. 4. During the feedbackphase, the pre-synaptic voltage will flip while the feedback circuitryholds PSE1 and PSE2 at their saturated values.

Over the course of the feedback phase, C11 receives a relatively largeaccumulation while C12 will receive none. When both the evaluate andfeedback phases are taken together, C11 receives a slightly largerupdate. In the next application of the input in state 1, PSE1 will again“win”, and a feedback phase will ensure a higher accumulated probabilityof connection formation on C11 than C12. This time, however, theaccumulated probability is slightly less for C11 that it was in theprevious frame. The reason is that the connection build up lowered theresistance on the C11 connection. This causes a higher current flux inthe next evaluate cycle.

Although both connections received an update, it is only the differencethat matters. As one can see from frames A, B, and C of FIG. 4. as thepost-synaptic activation increases, the accumulation returns to a setlevel comprising equal accumulations for both C11 and C12. As indicatedthus far, during the evaluate phase, there is no direct correspondencebetween the post-synaptic voltage and the force needed to emulate theplasticity rule as discussed above. For example, as the PSE's becomemore positive, the voltage difference between the pre-synaptic electrodeand post-synaptic electrode lessens, the electric field becomes weaker,and the attractive force dissipates. What we require is indeed just theopposite: as the post-synaptic voltage rises, the voltage differencebetween the pre- and post-synaptic electrodes needs to increase, therebyproviding the positive feedback required by our plasticity rule. We willaccomplish this by separating the read-out or evaluate phase from themodification or feedback stage.

As the post-synaptic neuron becomes increasingly activated, theprobability that the connection grows larger will decrease. We havecaptured the first aspect of the above mentioned plasticity rule, i.e,as y becomes larger, f(y) must decrease to zero. Without the feedbackphase, however, the direction of connection update is incorrect. Withonly an evaluate phase, the weight that contributes to the finalpost-synaptic neural state receives a smaller update. If this were tocontinue for only a small time, all connections would acquire equalvalues. To change the direction of the update, a simple operation can beperformed, i.e., flip the pre-synaptic value and lock the post-synapticvalue.

A clock signal cycles the neural circuitry between the evaluate andfeedback stage. FIGS. 5, 6 and 7 generally outline or summarize thisconcept. Note that in FIGS. 3( a)-3(d) and FIGS. 5, 6 and 7, identicalor similar parts or elements are generally indicated by identicalreference numerals. Circuit layout 302 of configuration 1 is depicted inFIG. 5, for example, along with associated output/evaluate and flip/lockfames. Similar features are depicted in FIGS. 6 and 7 for respectivecircuit layouts 301 and 303.

During the evaluate phase, the pre-synaptic electrodes are locked intoeither State 1 or State 2. The pre-synaptic electrodes can be seen as avoltage source driving a signal representative of either State 1 orState 2. We will refer to this as the Output stage, which is thepre-synaptic portion of the Evaluate phase. While the pre-synapticcircuitry is locked in the Output stage, the post-synaptic neuralcircuitry is locked in the Evaluate stage. In other words, while thepre-synaptic neuron is outputting, the post-synaptic neuron isevaluating. During this phase, the voltages generated by the Outputphase of the pre-synaptic neurons are driving the PSE of thepost-synaptic neural circuitry.

The post-synaptic neural circuitry provides a feedback mechanism thatpositively re-enforces the voltages seen on PSE1 and PSE2. In otherwords, the circuitry forces PSE1 and PSE2 into orthogonal states: if thevoltage on PSE1 is initially larger than the voltage on PSE2, thecircuitry further accentuates this difference until PSE1 and PSE2 isfully saturated at the supply rails. The circuitry that accomplishesthis will be discussed, but is not considered a limiting aspect of thepresent Invention. Indeed, there exist many circuits capable of thistype of positive re-enforcement. At the end of the Evaluate phase, thepre-synaptic neural circuitry flips the Output values state. In otherwords, if the Output stage was State 1, at the end of the Output phase,the pre-synaptic electrodes are driven to the complimentary state, orstate 2. We refer to this as the Flip stage of the Feedback phase.

As the pre-synaptic neuron enters the Flip stage, the post-synapticelectrode enters the Lock stage. The Lock stage effectively locks thepost-synaptic voltages in the state decided during the evaluate phase.This can be accomplished through additional circuitry or simply byallowing the continued action of the feedback circuitry. One can see theimmediate outcome of this setup: the state that is decided during theoutput/evaluate phase (i.e. receives more activation) is reinforced inthe feedback phase by increasing the electric field.

A series of logic gates can accomplish the above describedOutput/Evaluate, Flip/Lock phases. Although we have thus far onlydiscussed the case of one pre-synaptic electrode and two post-synapticelectrode, there are in fact more arrangements. We will now detail threepossible configurations, discuss the necessary feedback mechanism, andprovide example circuitry. With an understanding of the basicoutput/evaluate, flip/lock phases, the other electrode arrangements,there state encodings, and the feedback circuitry they require shouldbecome clear.

The quanta of update probability acquired during the feedback phase canbe matched to exactly balance the degradation due to increasing entropy.In other words, the probability that a nanoparticle will be removed fromthe electrode gap by random thermal motion can be balanced by theprobability gained from the feedback phase. This can in turn be used asa mechanism for temperature compensation or to simply gain more controlover the circuit parameters. By varying the time periods of both theevaluate and feedback phases, as well as changing the supply voltages,one can “dial in” the correct force, as well as adjust the learningrate. The consequences of such a feature are tremendous indeed. Althoughthe particles exist in a liquid, and the learning rate is a consequenceof particle dynamics within the liquid, the learning rate can still becontrolled electronically.

Because the power dissipation via resistive heating from the Knowm™connections is minimal, one could control the temperature of the chipindependently. This would allow for such things as teaching the chip ata higher speed (and higher temperature), and then processing real-timedata at a slower speed (and a lower temperature)

FIG. 8 illustrates a schematic diagram of a circuit 800 forconfiguration 1 described earlier, which can be implemented inaccordance with one embodiment. Similarly, FIG. 9 illustrates aschematic diagram of a circuit 900 for configuration 2 describedearlier, which can be implemented in accordance with another embodiment.Likewise, FIG. 10 illustrates a schematic diagram of a circuit 1000 forconfiguration 3 described earlier, which can be implemented inaccordance with an alternative embodiment. Note that in FIGS. 8-9,identical or similar parts are generally indicated by identicalreference numerals.

The first configuration (i.e., circuit 800) is essentially the same asthe prior example (i.e., circuit layout 302), but is described here forcompleteness and further clarity. Configuration 1 of circuit 800generally includes one pre-synaptic electrode per neuron and twopost-synaptic electrodes per neuron. The input is applied as a voltage,where a positive voltage, V₊, encodes one state and a lower voltage, V⁻,encodes the complimentary state. The signal is transferred to thepost-synaptic electrodes as a voltage on two differential electrodes.

Circuit 800 generally includes a plurality of electrodes 831, includingfor example, electrodes X1, X2, etc. and an A circuit 802 and a Bcircuit 804. The A circuit 802 is composed of tri-state inverters 806,808, an inverter 810 and an AND logic gate 812. The B circuit 804generally includes a pass gate 814 and a voltage keeper formed frominverters 816, 818. B circuit 804 also includes an XOR logic gate 821.Note that output from A circuit 802 is connected at node M to the inputof B circuit 804. Node M is generally connected to pass gate 814 of theB circuit 804. Circuit lines 844 and 846 of B circuit 804 representopposite voltage states. Circuit lines 840 and 842 associated with Acircuit 802 also represent opposite voltage states. Note that voltageand/or circuit values placed at circuit line 848, which is input to XORlogic gate 821 can be utilized to control flip functionality. Circuitline 850 generally comprises a PSE 1 while circuit line 852 generallyconstitutes a PSE2.

The voltage on Post-Synaptic Electrode 1 (PSE1) is compared with thevoltage on Post-Synaptic Electrode 2 (PSE2). The PSE with a greatervoltage determines the state of the neuron. By flipping the pre-synapticvoltage to the opposite voltage and locking the PSE voltages, westrengthen the connections that contributed to the final neural stateand weaken (via entropy) the connections that did not contribute. Thefeedback update is an “on or off” update, lacking incremental control,but of fixed and known quantity. By combining the accumulatedprobability of connection formation over both the evaluate and feedbackstage, we have succeeded in designing a circuit capable of providing afeedback that mirrors the above mentioned plasticity rule.

The circuitry to accomplish the Output/Evaluate and Flip/Lock phases isrelatively simple. Generally, there are two basic circuit blocks can bereferred to as circuit block “A” and circuit block “B” as indicatedpreviously herein. In FIG. 8, for example, circuit block “A” constitutescircuit 802 and circuit block “B” constitutes circuit 804. Both circuitblocks A and B form the post- and pre-synaptic functions of one neuron,respectively. Consequently, if a network does not contain more that oneneural layer, then both circuit blocks may not be required.

The function of circuit block A is two-fold. First, circuit block A(e.g., circuit 802) is responsible for the evaluate stage of theevaluate phase. Second, circuit block A is generally responsible for the“lock” stage of the feedback phase. In fact, only a very simple positivefeedback circuit may be required, as can be seen, for example, in theconfiguration depicted in FIG. 8. Because a neural module willeventually output on only one line, the addition of the inverter 810 onPSE2 and the AND gate 812 provides the following transfer function togenerate the voltage on node M, which is given as input to circuit blockB. Table 2 below illustrates some of these features:

TABLE 2 PSE1 PSE2 M 1 1 0 1 0 1 0 1 0 0 0 0

Circuit block A or circuit 802 depicted in FIG. 8, for example,generally includes the two tri-state inverters 806, 806, one inverter810 and one AND gate 812. When the tri-state inverters are activated,positive feedback is given to PSE1 and PSE2. As one can see, if PSE1 ishigh, then the inverter tries to bring PSE2 low, and visa versa. Whenthe inverters are inactive, their output floats and there is nofeedback. The evaluate and feedback phases can be generated byselectively activating the feedback circuit in the following mannerusing circuit lines 840 and 842. During the beginning of the evaluatephase, the feedback is shut off. this allows the voltage on PSE1 andPSE2 to build without feedback. These voltages are thus a representationof the activation as provided by the Knowm™ synapses. After this firststage of the evaluate phase, the feedback is turned on using, forexample, circuit lines 840 and 842.

The feedback forces the voltages on PSE1 and PSE2 into complementarystates determined by their initial value set in the previous stage. Inother words, the feedback amplifies the difference between PSE1 and PSE2voltages. When the lock stage is reached, the feedback circuitry ofcircuit 802 (i.e., the A circuit) simply remains on, thus keeping thevoltages at their previous value. At the end of the lock stage, thefeedback is turned off so as to provide a “reset” thereof. Note that theinverter 810 and the AND gate 812 can act to transfer the two-linerepresentation of two states to a one line representation of two states,as provided by the logic table above (i.e., Table 2)

Circuit block B (e.g., circuit 804) provides the pre-synaptic functionof the neurons. In the first stage of the evaluate phase, the circuit804 produces as an output the input it received during the previousstage. This output is representative of the output state of the neuronand was determined during the evaluate phase by circuit block A. (e.g.,circuit 802). After the first stage of the evaluate phase, the outputremains the same. In the first stage of the feedback phase, the outputflips. This functionality can be accomplished with, for example, passgate 814, a voltage keeper formed from inverters 816, 818, and XOR gate821 as depicted in configuration 1 of FIG. 8. Note that the XOR gate 821can be replaced by its compliment, as the choice is ultimatelyarbitrary.

Because the stages of the evaluate and feedback phases are controlled bya clock input, the relative widths of the evaluate and feedback phasesmay be changed electronically “on the fly”. The sizes of the transistorsmaking up the feedback circuitry may of course be modified to providethe best balance of chip real estate and functionality. Alternately, thestrength of the feedback may be modified electronically by changingvoltage biases. All that is reported here, for sake of clarity, is thefunctionality required. One example is provided herein, but manyvariations are of course possible.

FIG. 11 illustrates a schematic diagram of a circuit 1100, which can beimplemented in accordance with an embodiment. Circuit 1100 generallyincludes a plurality of A and B circuits including tri-state inverters1102, 1104, 1106 and 1108. Circuit 1100 also includes transistors 1109,1110, 1111, 1112, and 1114, which are connected to one another via acircuit line 1131. Additionally, tri-state inverters 1102, 1104, 1106and 1108 can be connected to one another via a circuit line 1130 andcircuit line 1132.

FIG. 12 illustrates a schematic diagram of a circuit 1200, which can beimplemented in accordance with an alternative embodiment. Circuit 1200also includes a plurality of A and B circuits along with tri-stateinverters 1202, 1204, 1206, 1208, 1210, 1212, 1212, 1214 and 1216, eachconnected to circuit lines 1240 and 1242 Circuit 1200 additionallyincludes transistors 1218, 1220, 1222, 1224, and 1226, which areconnected to one another via a circuit line 1240. A circuit control line1243 can be connected to transistors 1218, 1220, 1222, 1224, and 1226.

In addition to circuit block A and B described above, two pieces ofcircuitry can be utilized which are useful for the process of initiallyacquiring the independent component states. First, we must provide forlateral inhibition, or negative feedback between adjacent neuralmodules. This can be accomplished in exactly the same manner as incircuit block A, except this feedback is between adjacent circuitmodules. The purpose of the inhibitory (e.g., negative) feedback is tokeep adjacent neurons from acquiring the same IC state. The feedbackmust posses the ability to turn on and off (e.g., see components 1130,1132 in FIG. 11) and in fact is off for most of the post-learninglifetime of the chip. As an example, a tri-state inverter may be used toprovide negative feedback from PSE1 of one neural module to the PSE1 ofan adjacent neural module. Alternately, the feedback could be providedbetween PSE2 electrodes, or a non-inverting tri-state amplifier betweenPSE1 and PSE2 of adjacent neural modules. All that is required is thatone neuron is capable of pushing its neighbor into another state vialateral inhibition that can be turned on and off.

The second additional piece of circuitry could be as simple as onetransistor pulling either PSE1 or PSE2 to a pre-defined state (e.g.,voltage), which can be utilized to force a neuron into a known state. Inother words, this feedback would be used for a teaching signal, perhapscoming from another chip that has already acquired the states. Thisteaching signal is important for two reasons, although it is notstrictly necessary. The teaching signal can be used to train a group ofneural modules to recognize features within the data stream. Theknowledge of what constitutes an object is communicated to the chip viathe teaching signal, which is a global signal broadcast to all neuralmodules.

All the circuitry needed to provide the feedback required to emulate theplasticity rule given in equation (2) can be accomplished with theabove-mentioned circuitry. Not to loose generality, all that is requiredis circuitry capable of providing the mechanisms of synapticintegration, plastic feedback, lateral inhibition, and teaching. Theattraction of particles to the pre- and post-synaptic electrode gapscorrelate with an increased conductance. By providing an increasedvoltage difference to mirror a plasticity rule, the system canauto-regulate and converge to connection strengths suitable forinformation extraction.

Note that the electrode configurations 2 and 3 respectively depicted inFIGS. 9-10 are variations of the theme developed for configuration 1depicted in FIG. 8. The basic feedback stages essentially remain thesame. Configuration 2 (i.e., circuit 900) depicted in FIG. 9 forexample, is similar to configuration 1 (i.e., circuit 800) depicted inFIG. 8. In circuit 900 of FIG. 9, rather that one pre-synaptic electrodeand two post-synaptic electrodes, however, there are two pre-synapticand one post-synaptic electrode per neural module. Circuit 900 generallyincludes an A′ circuit 902 and a B′ circuit 904. The A′ circuit 902includes tri-state inverters 806 and 808, while the B′ circuit 904 iscomposed of the same components as the B circuit 804 depicted in FIG. 8,except for the addition of a inverter 908.

The post-synaptic electrode feedback circuitry of circuit 900 (i.e.,configuration 2) provides the same mechanism to saturate the voltage;however, this time a high voltage on the post-synaptic electrodeindicates State 1 (this is arbitrary) and a low voltage indicates State2. The following figure indicates circuit block A′, which provides thefeedback circuitry. As can be seen, the feedback circuitry is simply avoltage keeper circuit that can be regulated by the addition of atri-state inverter composing one or both of the inverters in the voltagekeeper formed from inverters 806 and 808. Circuit block B′ is thusidentical to that of configuration 1, with the addition of an extrainverter on the output to force two complimentary outputs instead ofjust one.

Note that lateral inhibition can be accomplished via a tri-stateinverter between adjacent post-synaptic electrodes. The teach signal islikewise accomplished by a transistor pulling a post-synaptic electrodeto ground or V_(cc) (e.g., see transistors 1109, 1110, etc. of FIG. 11).

Configuration 3 or circuit 1000 depicted in FIG. 10 simply combinesaspects of both configuration 1 and configuration 2 by representing boththe neural input and output on two electrodes. A pair of input linesdefines one “input channel” formed from a PSE1 line or electrode 1002and PSE2 line or electrode 1004. These input lines are driven to apositive voltage in an complimentary way:

State 1: Input 1 = Vcc Input 2 = Gnd State 2: Input 1 = Gnd Input 2 =Vcc

As with configuration 1, the process of neural integration can be viewedas a competition between Post-Synaptic Electrode 1 (PSE1) andPost-Synaptic Electrode 2 (PSE2).

Consider the case where an input channel is in state 1, so that inputline 1 (e.g., see X1 in FIG. 10) is “V_(cc)” and input line 2 (e.g., seeX1′ in FIG. 10) is “Gnd”. If we disregard the other inputs, the totalactivation of PSE1 is the result of the strength of the Knowm™connection connecting Input 1 and PSE1, which can be referred to as C11.Correspondingly, the total activation of PSE2 is the result of thestrength of the Knowm™ connection connecting Input 1 and PSE2, which canbe referred to as C12. The neural circuitry 1000 depicted in FIG. 10thus compares the two voltages on PSE1 and PSE2. If PSE1 is larger, theneuron is forced to output voltages on its output channel (e.g., node Min FIG. 10) characteristic of state 1. Alternately, if PSE2 is larger,the neuron is forced to output voltages on its output channel (e.g.,node M in FIG. 10) characteristic of state 2.

Based on the foregoing, it can be appreciated that four Knowm™connections can allow for 4-quadrant multiplication. Listed below is theconnection label, as described above, along with the transfer functionit facilitates:

Connection 11: State 1→state 1 Connection 12: State 1→state 2 Connection21: State 2→state 1 Connection 22: State 2→state 2

To further explain such circuitry, it should be noted that, given aninput in either state 1 or 2, the value of the 4 Knowm™ connections canencode either a “positive” weight:

Connection 11: Strong (many nanoparticles) Connection 12: Weak (no orfew nanoparticles) Connection 21: Weak Connection 22: StrongOr a “negative” weight:

Connection 11: Weak Connection 12: Strong Connection 21: StrongConnection 22: Weak

By the addition of a feedback mechanism (i.e., feedback circuitry), thefour connection values may take on a variety of values representinghighly “positive”, highly “negative”, or anywhere in between. It shouldbe noted that there exists a degeneracy in connections encoding aparticular value. This degeneracy is simply a result of four Knowm™connections being used to emulate a two-state system. The advantages ofthis could include noise immunity via the differential input lines,which are important for coupling at higher switching frequencies. Atwo-line representation can also provide a larger dynamic range for asignal, which may increase the noise margin. The circuitries needed toprovide the necessary feedback for circuit module A is identical tocircuit block A in configuration 1. Likewise, the circuitry required toimplement circuit block B is identical to circuit block B inconfiguration 2.

FIG. 13 illustrates a block-level circuit 1300, which can be implementedin accordance with one embodiment. Circuit 1300 generally includes ademultiplexer 1302 and a multiplexer 1304. A plurality of control lines1306 is connected to a plurality of A and B′ circuits 1310 and also aplurality of circuit lines 1320, which in turn are connected to aplurality of A and B′ circuits 1308 and a plurality of A and B circuits1312. Demultiplexer 1302 is connected to a plurality of electrodes 1314,while the A and B′ circuits 1308 are connected to a plurality ofelectrodes 1316. Additionally, a plurality of electrodes 1318 areconnected to the A and B′ circuits 1310 and the B and A circuits 1312.Note that the multiplexer 1304 is connected to a circuit line 1303,while the demultiplexer 1302 is connected to a circuit line 1301.

Knowm™ connections can form at the intersections of, for example, the B′and A electrodes, which are patterned on the surface of the chip. Inthis example, data can be streamed into the demultiplexer and applied asinput to one or more electrodes. If the data is streamed so as to outputthe compliment input vector (i.e. to achieve the flip function), then aB circuit is not required. Signals are integrated on the A electrodes ofcircuit module group 1308. The output of these modules is then appliedto the B′ electrodes. The signal is integrated via the A electrodes oncircuit module group 1310, where the pattern can be repeated foradditional layers. The output state of a neural module group can bemultiplexed and sent out on an output line 1303. The states of theneural circuit modules within a group can be used to determine thepresence of a feature in a data stream.

FIGS. 14 and 15 illustrate a high-level block diagram of a system 1400for independent component analysis, which can be implemented inaccordance with a preferred embodiment. In general, system 1400 includesa feedback mechanism 1406 and an electro-kinetic particle chain, suchas, for example, a Knowm™ connection of a Knowm™ network. The feedbackmechanism 1406 can be implemented in the context of, for example, thefeedback circuitry illustrated herein and which operates based on theplasticity rule described herein. The electro-kinetic induced particlechain 14306 interacts with the feedback mechanism 1406 in order toextract independent components from a data set as depicted in FIG. 14 byarrow 1402. ICA output data generated from system 1400 is indicated inFIG. 14 by arrow 1408. FIG. 14 represents one embodiment while FIG. 15represents another embodiment. The embodiment depicted in FIG. 15 showsthe addition of a neural module 1405.

Based on the foregoing, it can be appreciated that the Knowm™ systemsand methods disclosed herein is a new technology that extractsinformation from a data-stream. The information processed drives aplasticity rule that utilizes high-gradient-density electric fields toattract, and random thermal motion to repel, particles suspended in aliquid-interface above a traditional integrated electronic chip. Thestatistical regularities from the data stream is coupled to thealignment of nanoconnections between pre- and post-synaptic electrodes,which modifies their electrical resistance and in turn drives modularintegrated circuits. As indicated herein, a group of these circuits canbe made to extract the statistically independent components of a datastream. By processing information, a Knowm™ network, for example,remains stable in the face of random thermal motion and activelyre-configures its connections to changing conditions.

In general, when a particle is suspended in a solution and subjected toan electric field, the electric field induces a polarization in theparticle. If the field is homogeneous, the induced dipole aligns in thedirection of the field. If the field is inhomogeneous, the particle willexperience a force. The direction of the force is determined by thedielectric properties of the particle and suspension. If the particle ismore polarizable than the surrounding medium, the particle will feel aforce in the direction of increasing field gradient, which is termedpositive dielectrophoresis (pDEP). On the other hand, negativedielectrophoresis (nDEP) results when the medium is more polarizablethan the particle.

At low frequencies, charge accumulation at the particle/medium boundarycontributes to the induced dipole, which is referred to as theMaxwell-Wagner interfacial polarization and is a function of theparticle and medium conductivity. As the frequency is increased, thisterm of the polarization has increasingly less of an effect, as themobile charges do not have time to move an appreciable distance.

A conducting particle in a non-conducting liquid or gel will generallyfeel an attractive force toward the direction of increasing electricfield gradient. As the frequency of the applied electric field isincreased, the force transitions from an attractive force (pDEP) to arepulsive force (nDEP). It is therefore possible to use lowerfrequencies to attract a particle and higher frequencies to repel insuch a way as to build and break nanoconnections. It is also possible touse lower frequencies to attract and random thermal motion to breakconnections.

A Knowm™ device is a nano-scale electrical connection formed fromnanoparticles suspended in a liquid. The nanoparticles form sets ofconnections, called Knowm™ synapses. These synapses must be modified bya plasticity rule. We must provide a way to transfer voltages producedby neural circuit modules to a force that attracts the particles.Electrokinetic's is the theory used to describe the force that couplesthe plasticity rule to particle assembly.

Modern electronics operate by manipulating large numbers of electrons.The accumulations of electrons produce electric fields. Nano-electronicsseeks to use nano-scale devices to compute. A Knowm™ connection can bemanipulated with electric fields generated by traditional electronics. AKnowm™ system or device can therefore function as a bridge betweenmodern electronics and nano-electronics. Electrokinetic's makes suchdevices possible.

Generally speaking, modern electronics contain two components:transistors and the wires that connect them. The transistors are like amathematical function. They have an input and an output. By arrangingand building transistors in clever ways, they can be made to storeinformation. In almost all cases, modern electronics separatecomputation from memory.

Neural networks, such as a brain, also generally contain two components:neurons and the connections between them. The neurons are not unliketransistors. They too are like a mathematical function. The connectionsbetween neurons, i.e. synapses, are very different than the wiresbetween transistors. Synapses can change, which means they have amemory, and the way they change is governed by a plasticity rule.

The rule(s) is (are) simple. The rule takes as its input localinformation, and provides as its output the change in synapse strength.Knowm™ plasticity rules use two signals: the pre-synaptic signal and thepost-synaptic signal. These signals are provided as voltages onelectrodes.

Plasticity rules are capable of truly amazing feats of computation andadaptation. A Knowm™ network utilizes plasticity rules to accomplisheverything that is does. The rule assembles particles from a solution toform connections. The rule uses the information from a data stream tospontaneously set the connections at strengths that optimally extractinformation. The rule, using statistical regularities in the input datastream, repairs the connections if damaged by random thermal motion. Ifneural circuitry is damaged and becomes unreliable or unresponsive, therule re-wires the network to optimize performance.

Neural modules, built from simple CMOS (or equivalent technology), canbe utilized to provide feedback to pre- and post-synaptic electrodes.This feedback creates the electro-kinetic force that mirrors aplasticity rule capable of the above mentioned feats. The neural modulescontain less than 40 transistors. A group of these modules can be usedto isolate statistical regularities in a data stream. With today'stechnology, thousands of these module groups can be built on a singleintegrated circuit, along with billions of self-assembling connections.

A Knowm™ connection can be composed of many particles forming a bridgeacross pre- and post-synaptic electrodes. An individual particle in aliquid is not stable. The statistical properties of a group ofparticles, under the influence of a plasticity rule and random thermalmotion, is stable.

As transistor densities on modern integrated electronic chips increase,there is a growing trend toward reconfigurable architectures. Ratherthan implementing application specific integrated circuits (ASIC), adesign is deployed on programmable logic devices. The move is creating agrowing trend toward an IP-based development process, where circuits aredefined by their programming routine rather than the actual physicallayout. Rather than implementing a program to run on a processor, forexample, a chip can run a program to build the processor.

There are many ways to build such a system. One feature for constructinga programmable logic device is referred to as the grain size. As thedevice must be programmed, the question naturally arises as to what,exactly, is being programmed. Given a particular computational task, thedevice must use what resources are at is disposal to implement asolution. A course-grained architecture may implement a relatively smallnumber of complex modules, where each module contains an array ofvarious logic, memory, flip-flops and perhaps even entiremicroprocessors. As the architecture becomes finer, the complexity ofthe individual cell decreases as the number of the cells increase.

Perhaps the finest-grain architecture one might imagine is a block thatcan be programmed to implement any 2-input, 1-output logic gate. Byconstructing a vast array of Universal Logic Gates, one can envision asystem that can be programmed at a very fine scale, improving theultimate efficiency of the final circuit.

A hybrid CMOS/Knowm™ logic device is disclosed herein that can be“taught” to implement any of the 16 possible 2-input/1-output logicfunctions. The design is composed of a CMOS core of about 40transistors, as well as a Knowm™ synapse matrix formed above the CMOScore. The design is relatively space-efficient, considering the power ithas to implement any of the 16 total 2-input, 1-out logic functions. Anunderstanding of the process requires an understanding of the plasticityrule described herein under binary inputs, or more specificallyknowledge of the possible fixed-points or attractor states. Such aplasticity rule has been discussed previously.

Consider the configuration of FIG. 16, which illustrates a simple system1600 that includes a neuron 1602 with two inputs 1604 and 1606,respectively connected via two synapses 1608 and 1610. The neuron 1602may only output one of two states, but achieves a graded activation,defined by equation 1612 as y=w₁x₁+w₂x₂, where W_(i) is the weightconnecting the i^(th) input to the neuron 1602. The output 1614 fromneuron 1602 can be provided as f(y)=sign(y). The state of the neuron1602 can be seen as the sign (or state) of the activation.

The values of the synapses 1608 and 1610 can be allowed to evolve underthe auspices of the AHAH plasticity rule. There are many potentialtechniques for implementing the AHAH rule as a mathematical equation.The most general description of the feedback can be simply thefollowing: “The connection between pre-synaptic electrode A andpost-synaptic electrode B is modified in the direction that facilitatesthe transfer of electrode A's state to electrode B's state.”

For a digital application with two inputs, there are only four possibleinput patterns. For the moment, will refer to the states as “+1” and“−1” rather than “1” and “0”. This is because the explicit sign of theinput is important for AHAH modification. The four possible inputpatterns are:[+1,+1], [+1,−1], [−1,+1], [−1,−1].  Dataset 1

It can be verified that the stable weight vectors resulting from theapplication of these four input patterns under the AHAH plasticity ruleare provided as: [w₁, w₂]=[0,+1],[0,−1],[+1,0],[−1,0].

Such states can be referred to as S1 though S4, respectively. Thefollowing logic tables indicate the output of a neuron in each of thefour possible states. Note that S1=X2, S2=˜X2, S3=X1 and S4=˜X1, where“˜” indicates the logical compliment.

TABLE 3 S1 S2 S3 S4 [0, +1] [0, −1] [+1, 0] [−1, 0] X1 X2 S1 X1 X2 S2 X1X2 S3 X1 X2 S4 1 1 1 1 1 −1 1 1 1 1 1 −1 1 −1 −1 1 −1 1 1 −1 1 1 −1 −1−1 1 1 −1 1 −1 −1 1 −1 −1 1 1 −1 −1 −1 −1 −1 1 −1 −1 −1 −1 −1 1

One can view the output of a neuron under the influence of the AHAH ruleand processing the dataset 1, as either passing or inverting one of thetwo inputs, depending on its state. To aid in all future discussion, wewill make the substitution −1→0 to conform to standard convention. It isimportant, however, to view “0” as a state, rather than a number, sincemultiplication by zero is zero and therefore not representative of theAHAH rule. To achieve useful logic functions, we can take two neurons,each occupying a state, and NAND their outputs.

FIG. 17 illustrates a system 1700 that generally includes a logic gate1702 having an output 1704. Logic gate 1702 receives inputs respectivelyfrom the output of neurons N1 and N2 depicted in FIG. 17. Depending onthe state of the neurons, the output will follow the rules of variouslogic functions. This can be seen in table 4, where the functionality ofcircuit 1700, shown in FIG. 17, can be tested for logic functionality.

TABLE 4 [S1, S2] [X1, X2] [1, 1] [1, 2] [1, 3] [1, 4] [2, 1] [2, 2] [2,3] [2, 4] [3, 1] [3, 2] [3, 3] [3, 4] [4, 1] [4, 2] [4, 3] [4, 4] [1, 1]0 1 0 1 1 1 1 1 0 1 0 1 1 1 1 1 [1, 0] 1 1 1 1 1 0 0 1 1 0 0 1 1 1 1 1[0, 1] 0 1 1 0 1 1 1 1 1 1 1 1 0 1 1 0 [0, 0] 1 1 1 1 1 0 1 0 1 1 1 1 10 1 0 Logic 11 1 9 3 1 6 5 2 9 5 13 1 3 2 1 4 Gate

Where the logic gates have been numbered according to the followingscheme:

TABLE 5 Logic [1, 1] [1, 0] [0, 1] [0, 0] Gate 1 1 1 1 1 1 1 1 0 2 1 1 01 3 1 1 0 0 4 1 0 1 1 5 1 0 1 0 6 1 0 0 1 7 1 0 0 0 8 0 1 1 1 9 0 1 1 010 0 1 0 1 11 0 1 0 0 12 0 0 1 1 13 0 0 1 0 14 0 0 0 1 15 0 0 0 0 16

As an example, under this numbering scheme, XOR=“10”, AND=“8” andOR=“9”. As can be seen, circuit 1700 is not capable of implementingevery logic function, since the state [S1, S2] is equivalent to [S2,S1]when “NANDed”. Such a situation can create degeneracy in logicfunctionality in that differing neural states can lead to the same logicfunction. One could replace the NAND gate with a NOR gate and achievesimilar results. In all cases, because of the degeneracy, even thoughtwo neurons are capable of occupying 16 distinct states, differentneuron states still can lead to the same logic function (degeneracy).The following table lists the following attainable logic functions forvarious “extractor logic gates”. In other words, the NAND gate incircuit 1700 could be replace with a NOR gate.

TABLE 6 Attainable Logic Extractor gate Functions NAND 1, 2, 3, 4, 5, 6,9, 11, 13 NOR 4, 8, 11, 12, 13, 14, 15, 16 XOR 1, 7, 10, 16

It is unfortunate that circuit 1700 does not attain the XOR function(Logic functions 7 and 10). To attain a greater gate functionality, thecircuitry should be modified slightly. It is certainly possible toconsider a circuit composed of three neurons and two NAND gates. Thatis, three neurons NANDed together or the output of two NANDed neuronsNANDed with a third neuron. However, this gate offers little benefitfrom circuit 1700. To achieve true universal logic function, a fourneuron implementation is preferred, which is composed of 2 instances ofcircuit 1700.

Note that in a physical implementation, each input line is representedon a differential electrode pair, as seen in FIGS. 3 a-3 c. Thedifferential representation can be seen explicitly in FIG. 18, whichdepicts a system 1800 that includes logic gates 1702, 1804 and 1806.Note that in FIGS. 17-20, identical parts or elements are generallyindicated by identical reference numerals. In system 1800, X1 and X2inputs are provided to neurons N1 and N2 and to neurons N3 and N4.Output from neurons N1 and N2 is provided to logic gate 1702 whoseoutput 1704 is input to logic gate 1806. Similarly, the output fromneurons N3 and N4 is provided as input to logic gate 1804 whose output1805 is provided as input to logic gate 1806. Output from logic gate1806 is provided at output 1804.

It can be demonstrated that universal logic functionality can be foundin various subspaces in the neural states. This allows designers tosimplify the circuitry considerably so that universal logic function canbe attainable with relatively little circuit overhead. Table 7 lists thelogic gate function for all 256 possible input states. The table hasbeen ordered by logic gate hierarchies.

Each neuron in the circuit 1800 can occupy four states, which we haveshown previously. There are therefore 4⁴=256 possible statecombinations. The following table lists all 256 possible stateconfigurations, as well as the over-all circuit 1800 logic function. Asone can see, multiple states lead to the same logic function. This time,however, every possible logic function can be attained.

TABLE 7 Logic S1 S2 S3 S4 Gate 1 1 2 2 1 2 2 1 1 1 3 3 4 4 1 4 4 3 3 1 11 2 3 2 1 1 3 2 2 1 1 3 3 2 1 4 3 3 2 2 3 1 1 2 3 2 1 1 2 3 3 1 1 2 3 31 4 2 3 3 4 1 2 4 1 3 3 2 1 3 2 2 3 2 2 1 3 3 2 2 3 1 3 2 2 3 3 3 2 4 33 3 3 1 2 2 3 3 3 2 2 3 3 3 2 4 3 3 3 4 2 3 4 2 3 3 3 1 2 3 3 4 1 3 2 34 1 3 3 2 4 1 3 3 3 4 2 1 3 3 4 2 3 1 3 4 2 3 3 1 4 2 3 3 3 4 3 1 2 3 43 1 3 2 4 3 1 3 3 4 3 2 1 3 4 3 2 3 1 4 3 2 3 3 4 3 3 1 2 4 3 3 1 3 4 33 2 1 4 3 3 2 3 4 3 3 3 1 4 3 3 3 2 4 3 3 3 3 4 3 3 3 4 4 3 3 4 3 4 3 43 3 4 4 3 3 3 4 1 1 2 4 5 1 1 4 2 5 1 1 4 4 5 1 3 4 4 5 2 4 1 1 5 3 1 44 5 4 2 1 1 5 4 4 1 1 5 4 4 1 3 5 4 4 3 1 5 1 1 1 1 6 1 1 1 2 6 1 1 1 36 1 1 1 4 6 1 1 2 1 6 1 1 3 1 6 1 1 3 4 6 1 1 4 1 6 1 1 4 3 6 1 2 1 1 61 3 1 1 6 1 3 1 4 6 1 3 4 1 6 1 4 1 1 6 1 4 1 3 6 1 4 3 1 6 2 1 1 1 6 31 1 1 6 3 1 1 4 6 3 1 4 1 6 3 4 1 1 6 4 1 1 1 6 4 1 1 3 6 4 1 3 1 6 4 31 1 6 1 3 2 4 7 1 3 4 2 7 2 4 1 3 7 2 4 3 1 7 3 1 2 4 7 3 1 4 2 7 4 2 13 7 4 2 3 1 7 1 2 1 3 8 1 2 3 1 8 1 3 1 2 8 1 3 1 3 8 1 3 2 1 8 1 3 3 18 1 3 3 4 8 1 3 4 3 8 2 1 1 3 8 2 1 3 1 8 3 1 1 2 8 3 1 1 3 8 3 1 2 1 83 1 3 1 8 3 1 3 4 8 3 1 4 3 8 3 4 1 3 8 3 4 3 1 8 4 3 1 3 8 4 3 3 1 8 14 2 2 9 2 2 1 4 9 2 2 4 1 9 2 2 4 4 9 2 3 4 4 9 3 2 4 4 9 4 1 2 2 9 4 42 2 9 4 4 2 3 9 4 4 3 2 9 1 4 2 3 10 1 4 3 2 10 2 3 1 4 10 2 3 4 1 10 32 1 4 10 3 2 4 1 10 4 1 2 3 10 4 1 3 2 10 1 2 2 2 11 2 1 2 2 11 2 2 1 211 2 2 2 1 11 2 2 2 2 11 2 2 2 3 11 2 2 2 4 11 2 2 3 2 11 2 2 3 4 11 2 24 2 11 2 2 4 3 11 2 3 2 2 11 2 3 2 4 11 2 3 4 2 11 2 4 2 2 11 2 4 2 3 112 4 3 2 11 3 2 2 2 11 3 2 2 4 11 3 2 4 2 11 3 4 2 2 11 4 2 2 2 11 4 2 23 11 4 2 3 2 11 4 3 2 2 11 1 2 2 3 12 1 2 3 2 12 2 1 2 3 12 2 1 3 2 12 23 1 2 12 2 3 2 1 12 2 3 2 3 12 2 3 3 2 12 2 3 3 4 12 2 3 4 3 12 3 2 1 212 3 2 2 1 12 3 2 2 3 12 3 2 3 2 12 3 2 3 4 12 3 2 4 3 12 3 4 2 3 12 3 43 2 12 4 3 2 3 12 4 3 3 2 12 1 2 4 4 13 1 4 2 4 13 1 4 4 2 13 1 4 4 4 132 1 4 4 13 2 4 1 4 13 2 4 4 1 13 2 4 4 4 13 3 4 4 4 13 4 1 2 4 13 4 1 42 13 4 1 4 4 13 4 2 1 4 13 4 2 4 1 13 4 2 4 4 13 4 3 4 4 13 4 4 1 2 13 44 1 4 13 4 4 2 1 13 4 4 2 4 13 4 4 3 4 13 4 4 4 1 13 4 4 4 2 13 4 4 4 313 4 4 4 4 13 1 2 1 4 14 1 2 4 1 14 1 4 1 2 14 1 4 1 4 14 1 4 2 1 14 1 43 4 14 1 4 4 1 14 1 4 4 3 14 2 1 1 4 14 2 1 4 1 14 3 4 1 4 14 3 4 4 1 144 1 1 2 14 4 1 1 4 14 4 1 2 1 14 4 1 3 4 14 4 1 4 1 14 4 1 4 3 14 4 3 14 14 4 3 4 1 14 1 2 2 4 15 1 2 4 2 15 2 1 2 4 15 2 1 4 2 15 2 4 1 2 15 24 2 1 15 2 4 2 4 15 2 4 3 4 15 2 4 4 2 15 2 4 4 3 15 3 4 2 4 15 3 4 4 215 4 2 1 2 15 4 2 2 1 15 4 2 2 4 15 4 2 3 4 15 4 2 4 2 15 4 2 4 3 15 4 32 4 15 4 3 4 2 15 1 2 1 2 16 1 2 2 1 16 1 2 3 4 16 1 2 4 3 16 2 1 1 2 162 1 2 1 16 2 1 3 4 16 2 1 4 3 16 3 4 1 2 16 3 4 2 1 16 3 4 3 4 16 3 4 43 16 4 3 1 2 16 4 3 2 1 16 4 3 3 4 16 4 3 4 3 16

A CIRCUIT 1800 gate may certainly be utilized to achieve areconfigurable universal logic device. By setting the neural states,Table 7 shows that any logic gate can be attained. One problem, however,is the redundancy. Four neurons, each capable of occupying 4 states,lead to 256 possible combinations. To achieve universal logic function,we only need 16, or two neurons. By evaluating Table 7, one can identifya subspace of neural states where two out of the four neurons states donot change. In this way, we only need change the states of two neurons.Take, for instance, the case where Neuron 1 (N1) is in State 1 andNeuron 2 (N2) is in state 2. In this case, we can find the followingsubspace in Table 8:

TABLE 8 S1 S2 S3 S4 LF 1 1 2 1 6 1 1 2 2 1 1 1 2 3 2 1 1 2 4 5 1 2 2 116 1 2 2 2 11 1 2 2 3 12 1 2 2 4 15 1 3 2 1 8 1 3 2 2 3 1 3 2 3 4 1 3 24 7 1 4 2 1 14 1 4 2 2 9 1 4 2 3 10 1 4 2 4 13

Multiple subspaces can be found in table 7 that cover all logicfunctions. Table 9 shows one more example, where neuron two is in state1 and neuron 4 is in state 2.

TABLE 9 S1 S2 S3 S4 LF 1 1 2 2 1 1 1 2 3 2 1 1 4 2 5 1 1 1 2 6 2 1 2 211 2 1 3 2 12 2 1 4 2 15 2 1 1 2 16 3 1 2 2 3 3 1 3 2 4 3 1 4 2 7 3 1 12 8 4 1 2 2 9 4 1 3 2 10 4 1 4 2 13 4 1 1 2 14

Recall that the four possible states can be seen as a device functionthat either passes or inverts one of the inputs. We may use this to ouradvantage so as to illuminate the redundant circuitry. We have shown howvarious configurations can be used to implement a Knowm™ synapse thatencodes both a state and a magnitude. For the following example, we willuse the configuration of two pre-synaptic electrodes and onepost-synaptic electrode per synaptic junction. In this configuration,pre-synaptic signals are represented by differential electrode pairs:X1, ˜X1 and X2, ˜X2, where ˜ indicates the logical complement.

Given the differential representation, one can see how a neural statecan be permanently emulated by a direct connection to one of the inputlines. For example, Neural State 1 is consistence with a directconnection to X2 and Neural State 2 is consistent with a directconnection to ˜X2. To take advantage of the logic subspace shown in thetables above, as well as the differential pre-synaptic electrodeconfiguration, we may simplify the circuitry as shown in system 1900 ofFIG. 19.

By application of a teaching and a teach-enable signal, it is a simplematter to initialize the neurons in the ULG into the desired states.Indeed, teaching is simply the process of forcing a neuron into apre-determined state. We may do this by selectively charging orgrounding the post-synaptic electrodes. To achieve independent controlover all neuron states within the ULG, a separate teaching could be usedfor each neuron. This would require 2 teach input lines, 1 teach enableline, as well as the two input and one output line. There are many waysto initialize the neural states. We will describe one such way as anillustration of the kind of data-stream manipulations that are possible.It should be apparent from this that there are many possibilities.

Consider a subspace where the state of neurons 2 and 4 determine thelogic function of the ULG. Further consider a DataStream composed of thedata vectors:[1,1],[1,−1],[−1,1],[−1,−1]

To initialize a neuron into logic function 6, for example, we wouldprovide training signals consistent with neural state 1 for both N1 andN2. If the input vectors undergo a rotation, or a series ofsubstitutions, then we can emulate another neural state. To illustratethis, consider that the output of a neuron in state 1, when subjected tothe data vectors above, will generate the following output: 1, −1, 1,−1. If we wanted to initialize N1 into state 1, but N2 into state 2,then we could present the data vector set [1,1],[1,−1],[−1,1],[−1,−1] toN1 and the data vector set [1, −1], [1,1], [−1,−1], [−1,1] to N2. Inthis way, each neuron is receiving the same training signals, but theinputs have undergone a transformation so that N1 is receiving trainingsignals consistent with state 1 and N2 state 2. One complete circuitdiagram capable of this can be seen in FIG. 20, which illustrates asystem 2000 that functions as a universal logic gate (ULG).

System 2000 generally includes two input terminals 2002 and 2004 towhich respective inputs 1 and 2 can be provided. Input 1 (i.e., input2002) and input 2 (i.e., Input 2004) can be provided as binary voltagesat input terminals 2002 and 2004, respectively. Inverters 2014 and 2018provide the inverted, or compliment, voltage signal so as to representthe inputs on a differential electrode pair, discussed in FIGS. 3 a-3 c.Knowm™ connections 2006, 2008, 2010 and 2012 provide a resistiveconnection to one input electrode of NAND logic gate 1702. Likewise,Knowm™ connections 2020, 2022, 2024 and 2026 provide a resistiveconnection to one input electrode of NAND logic gate 1804. Via 2016provides a direct connection to one input electrode of NAND 1702.Likewise, Via 2018 provides a direct connection to one input electrodeof NAND 1804.

A tri-state voltage keeper circuit, provided by inverters 2036 and 2034,can provide a positive feedback signal capable of saturating theelectrode voltage when activated by the evaluate enable control lines.Likewise, a tri-state voltage keeper circuit, provided by inverters 2038and 2040 provide a positive feedback signal capable of saturating theelectrode voltage when activated by the evaluate enable control lines.Transistors 2030 and 2032 may provide a conducting path between teach 1and teach 2 control lines and there respective electrodes when activatedby a teach enable control line. NAND logic gates 1702, 1804 and 1806provide a logical transformation of the four input lines. Circuit 2048provides for a routing circuit capable of directing either the output ofinverter 2045 or the output of NAND 1806 to output line 2050. Circuit2048 can provide a logic bypass so as to implement a flip cycle forsecond-level logic.

To understand why the output must change while the training signal isapplied, so as to explain circuit 2048, it is necessary to understandthe flip/lock cycle, which has been previously discussed. To summarize,it is necessary for the pre-synaptic electrode to flip states if theflip/lock cycle is to properly emulate the AHAH rule. If more than oneULG are connected together, so that the output of one ULG is the inputto another, then we must insure that a configuration exists so that theoutput of the first ULG flips states. If one looks at the state diagramsof Table 3 it is apparent that these states satisfy this requirement. Inother words, whatever input vector one may choose, and in whatever statethe neuron may be, if one takes the compliment vector, the output of theneuron is guaranteed to flip states. In this way, if the output of theULG is made so that the NAND circuitry is bypassed, when the input tothe ULG is flipped the output will also flip. The importance of this isthat a ULG connected to the first ULG will receive the flip state, whichallows the AHAH plasticity rule to be properly implemented via theflip/lock cycle. It may also be convenient to have independent controlover the NAND bypass. In this case, one can control this via anindependent control line, rather than linking it to the teach enablecontrol line.

Based on the foregoing, it can be appreciated that a universal logicgate apparatus is disclosed, which include a plurality ofself-assembling chains of nanoparticles having a plurality of resistiveconnections, wherein the plurality of self-assembling chains ofnanoparticles comprise resistive connects utilized to create Aplasticity mechanism is also provided, which is based on a plasticityrule for creating stable connections from the plurality ofself-assembling chains of nanoparticles for use with the universal,reconfigurable logic gate. The plasticity mechanism can be based, forexample, on a 2-dimensional binary input data stream, depending upondesign considerations. A circuit is also associated with the pluralityof self-assembling chains of nanoparticles, wherein the circuit providesa logic bypass that implements a flip-cycle for second-level logic.Additionally, an extractor logic gate is associated with the pluralityof self-assembling chains of nanoparticles, wherein the extractor logicgate provides logic functionalities.

It will be appreciated that variations of the above-disclosed and otherfeatures and functions, or alternatives thereof, may be desirablycombined into many other different systems or applications. Also thatvarious presently unforeseen or unanticipated alternatives,modifications, variations or improvements therein may be subsequentlymade by those skilled in the art which are also intended to beencompassed by the following claims.

1. A discrete-state synapse apparatus, said apparatus comprising: aplurality of conducting channels under the influence of a plasticityrule, where each channel among said plurality of conducting channels iscapable of being in two or more states with different electricalresistances thereof; wherein at least one transition between conductingstates of said plurality of conducting channels is susceptible tothermal energy fluctuations; wherein at least one transition betweenconducting states of said plurality channels is susceptible to anapplied voltage bias; and at least one differential pair of channels ofsaid plurality of conducting channels forming two parallel resistiveconnections comprising two conducting pathways.
 2. The apparatus ofclaim 1 wherein said at least one differential pair of channels isformed from a configuration of an input electrode and two outputelectrodes.
 3. The apparatus of claim 2 wherein a state of saidapparatus is measured by applying an electric potential on said inputelectrode while measuring the differential electric potential on saidtwo output electrodes.
 4. The apparatus of claim 2 wherein a state ofsaid apparatus is reinforced by applying a positive feedback betweensaid two output electrodes and inverting an electric potential polarityof an input potential.
 5. The apparatus of claim 1 wherein said at leastone differential pair of channels is formed from a configuration of twoinput electrodes and one output electrode.
 6. The apparatus of claim 5wherein a state of said apparatus is measured by applying a differentialelectric potential on the input electrodes while measuring the electricpotential on said two output electrodes.
 7. The apparatus of claim 5wherein a state of said apparatus is reinforced by applying a positivefeedback on said two output electrodes and inverting an electricpotential polarity of said input electrode.
 8. The apparatus of claim 1wherein said differential pair of channels is formed from aconfiguration of two input electrodes and two output electrodes.
 9. Theapparatus of claim 8 wherein a state of said apparatus is measured byapplying a differential electric potential on said two input electrodeswhile measuring a differential electric potential on said two outputelectrodes.
 10. The apparatus of claim 8 wherein a state of saidapparatus is reinforced by applying a positive feedback between said twooutput electrodes and inverting an electric potential polarity of saidtwo input electrodes.
 11. The apparatus of claim 1 wherein relativetemporal widths of an evaluate phase and a feedback phase aredynamically adjusted.
 12. A neural node apparatus, comprising: aplurality of discrete-state synapses sharing a same electrode, saiddiscrete-state synapses under the influence of a plasticity rule;wherein a state of said neural node apparatus is measured by applying anelectric potential on at least one input electrode of at least onediscrete-state synapse among said plurality of discrete-synapses, whilemeasuring a differential electric potential on a shared output electrodethereof; and wherein a state of said neural node apparatus is reinforcedby applying a positive feedback on at least one output electrode whileinverting an electric potential polarity of said at least one inputelectrode of said at least one discrete-state synapse so as tofacilitate a transfer of discrete-state synaptic states to a node stateof said neural node apparatus.